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When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared to when a constant force is applied. Work is the product of force and displacement, while energy is the capacity of a system to do work. When a constant force is applied to an object, the work done can be calculated as the product of the force and the distance moved in the direction of the force. However, when a variable force is applied, the...
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Harnessing non-equilibrium forces to optimize work extraction.

Kristian Stølevik Olsen1, Rémi Goerlich2,3, Yael Roichman3,4

  • 1Institut für Theoretische Physik II - Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany. kristian.olsen@hhu.de.

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|December 9, 2025
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Summary
This summary is machine-generated.

Researchers found optimal control strategies can minimize energy costs in microscopic systems by exploiting non-equilibrium forces. This work provides analytical solutions for optimal protocols and work, enhancing energy efficiency in nano- and microscale devices.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Optimal Control Theory

Background:

  • Optimal control theory minimizes energetic costs in noisy microscopic systems.
  • Exploiting the temporal structure of non-equilibrium forces presents an opportunity for enhanced efficiency.

Purpose of the Study:

  • To derive exact analytical forms for optimal protocols and work in non-equilibrium systems.
  • To establish a general quasistatic bound on work based on integrated forces.
  • To demonstrate how optimal protocols utilize information about non-equilibrium forces and initial states.

Main Methods:

  • Derivation of exact analytical solutions for optimal control protocols.
  • Development of a general quasistatic work bound.
  • Analysis of systems with periodic driving forces and active matter.

Main Results:

  • Exact analytical forms for optimal protocols and work were obtained for any driving force and duration.
  • A general quasistatic bound on work was derived, depending only on integrated force characteristics.
  • Optimal protocols were shown to leverage information about non-equilibrium forces and initial state measurements for work extraction.

Conclusions:

  • Exploiting the temporal structure of non-equilibrium forces offers a powerful, largely unexplored approach for energy efficiency.
  • The derived methods provide new directions for designing adaptive, energy-efficient strategies in noisy, time-dependent microscopic systems.
  • This approach promises significant performance gains in nano- and microscale devices.